Graphical Interface for modelling the electric field and ionic charge distribution in biological tissue

Daniela O.H. Suzuki¹, Airton Ramos^1,2, Jefferson L.B. Marques^1
1Institute of Biomedical Engineering (IEB), Department of Electrical Engineering (EEL),
Federal University of Santa Catarina (UFSC) ,Florianópolis-SC, Brazil, 88040-900,
²Department of Electrical Engineering, Center of Technological Sciences,
State University of Santa Catarina (UDESC), Joinville-SC, Brazil, 89223–100.

Abstract: The method for electric field and ionic charge density distributions calculation in biological tissue based on an equivalent electric circuit model have the main advantages: simple to model inhomogeneous and anisotropic environment (in relation to the dielectric permittivity and transport properties) and time domain electric field and ionic charge distribution calculation, considering the time and spatial variations of the electrical conductivity. The program for graphical simulation comes to create a fluent and visual interface to the user. It takes advantage of the intrinsic simplicity of the equivalent electric circuit method to perfect the understanding of the results and to present graphical outputs and clear interactions with the user to facilitate the data input. The objective of this study is through the resources of the graphical simulation program, provide a wider use of the software to improve the planning of the experimental and therapeutical studies, besides the reduction of the risks of the subjects involved in the studies related to the biological effects of electromagnetic fields.

INTRODUCTION

The bioelectromagnetism area has been studied researched by the beneficial and harmful effects that the electromagnetic fields can cause on biological systems. In the last decades there was a great interest in that area, the researches and the number of papers are developing so fast. Studies of theories, models, technologies, new devices appeared to bring us knowledge about the effects of the electromagnetic fields. 

The mathematical model of the magnetic fields effects in the biological environment does not reply and neither explain the experimental observations found at the experimental research models. Among the several authors that present theoretical models to explain this effect it can be mentioned the work presented by DeBruin and Krassowska [1,2]. Where the authors present a model to investigate the electroporation effect in a single cell, considering the ionic concentration effects, field force and rest potential. 

This need for a model that provides a more intimate relationship between the theory and the experimentation was presented by Ramos et al. (2001, 2000), a model that contemplates the representation of biological tissue through the method of equivalent circuit for analysis of electric field distribution and ionic charger. 

The simulation program proposed in this work is based on the Ramos et al. [3, 4] model in the implementation of a system that presents graphic inputs and presentations of the results to turn it more versatile and interactive. In addition, the program becomes useful for several different situations, as the simulation for the effect by a external electric field in several types of tissue.

METHODS

The Equivalent Electric Circuit Model in Low Frequencies

We divided the volume on analysis in numerous and small blocks with the parallelepiped shape.  The union of each block, corresponding to a node of the electric circuit, it is done by a group of paralleled circuits elements. The elements are classified and compared with a biological environment in the following way: displacement current, capacitance; for each different electric charge in the environment: a conductance represents a conduction current and a current source corresponding the diffusion current. Each element is calculated based on the dimension of the blocks and the electric and transport properties in that point of the space. Therefore, the total current leaving the node ‘j’ of the circuit is given by:

(1)

C is the capacitance, g is the conductance and k is the coefficient of diffusion of the block. Between node ‘j’ and  adjacent node in each direction we calculated the electric potentials and density of ionic charge, dV and dr. The summation includes all the ‘n’ different ionic types present in the environment and the three directions of the space (i=x,y,z). The electric field and charge distribution in the time now it can be obtained by solving the resulting circuit electric of the tissue in study, for given initial and boundary conditions. The ionic density is updated to each step based on the difference between the input and output ionic currents for each circuit node. 

One of the points of interest in the studies of electromagnetic fields on tissue biological  is in the interfaces that are transition areas between two other different conductivity and permittivity areas. Because of the conductivity difference, the close concentration gradients of the interfaces, in general, are much more intense than far away from them. Therefore, the interface areas are the “critical  points” in the numeric analysis of the distribution of fields and charge. The model proposed by Ramos et al. [3, 4] search a separation between neighboring nodes of this space of different form. The use of regular mesh in the cases of curvilinear surfaces doesn't allow a good representation of the surface, a better alternative it is the use of an irregular mesh where the nodes are distributed evenly on the surface. It  allows a better definition of the characteristics presented like this in those areas. 

In this study, the influence of the magnetic field was not considered produced by the ionic currents. Therefore, the proposed model is just been worth in low frequencies.

The simulations Software

This work comes as a tool that supplies several facilities that turn the simulation of the application of magnetic fields in tissue and biological systems simpler and practical. We introduced alternatives that help to maximize the simplification of the specifications of the data for the simulation. 

The data input has graphic interface that makes possible the user to select and input the dielectric permittivity and transport properties, building the biological system in a simple and fast way. These illustrations can represent as much cells as tissue, depending on the simulation level for this program, that is, in case of local analysis of the data will be defining in the graphical environment portions of cellular level. While in the macroscopic analysis, already with the electric characteristics defined in the local analysis, the visual interface should expose the concepts at level of biological tissue. 

The intention is to propose to the user a way easier to specify real forms of cells and tissue. For this the user should not take a long period of time learning how to use the program, we will propose some items as a pattern; the exhibition of information more used by the user to define the environment, e.g., conductance, density of ionic charge, region conductance, among other measures that should be present in the screen to facilitate the specification of parameters, at local level as well as at macroscopic level; facilitating the approximation of the real biological environment with known geometric forms, as rectangles, circles, spheres, cylinders, etc. 

All the necessary functions to total initialization of the parameters should be intuitive and provided helps, in case the user is not used to the program. 

For the specifications in the ways of real tissue the program supplies the possibility to capture images of other sources (e.g. electronic microscopes), introducing the possibility to simulate real images. With that we can minimize the mistakes in the calculations for practical systems, it increases the reliability and fidelity of the graphs and data presented by the program. 

One of the important parts data input is the partition of the transition areas, i.e., to define the regions with high resolution. This transition areas are very delicate situation, because too much increase of areas of high resolution can increase  the computational calculation time. The selected areas have a criterion that takes in consideration the dimension of the space among cells, i.e, the mesh will be finer as the distance between nodes is smaller. That partition will be shown in the graphic screen so that the user can have the clear disposition in that the mesh was distributed, facilitating the discovery of areas of unnecessary high resolution. 

It is intended with this work to present graphical outputs of field intensity and current of 2D and 3D systems biological, in a simple and clear way for the solution of concrete problems, making possible a consistent progress for the use of electroporation, through the use of a graphical environment.

RESULTS and DISCUSSION

The mathematical improvement of the program, to speed up the computational processes will be worked in another study. But the idea is at first to use available computers in the market, without the need of parallel computation, nor computational setup that impede the use of the program in personal computer.  

The principal objective of this work is to transmit through an interactive environment and available graphical resources, a visual language that communicates fluently, subtle and direct with the user. It presents in a clear way the results of the simulation in graphs that condense fast visual analysis and necessary data is displayed. The flexibility of data input supplied by the own method of the electric equivalent circuit is enlarged by a visual data input, that stores some data of standard biological environment, where the ionic concentrations are specified for each area. This does not exclude the user the possibility to alter the concentrations and even the íons of each environment, differentiating internal and external regions. 

As the electroporation process is not yet very well understood, the investigation through the simulation of the real situations can provide precious information. The simulation program will bring many benefits for several areas, that can get better understanding of the application of and /or effects of electromagnetic fields on biological tissue.

REFERENCES

[1] DeBruin, K.A. and Krassowska, W. Modeling eletroporation in a single cell.I. Effects of field strength and rest potencial. Biophys.J. 77:1213-1224, 1999.

[2] DeBruin, K.A. and Krassowska, W. Modeling eletroporation in a single cell.II. Effects of ionic concentrations. Biophys.J. 77:1225-1233, 1999.

[3] Ramos, A., Raizer, A. and Marques, J.L.B. 2000. “Modelling the electric field e ionic charge distribution in biological tissue through the equivalent electric circuit method”, in 3^rd ICBEM, 2000, pp. 41-42.

[4] Ramos, A., Raizer, A. and Marques, J.L.B. 2001. “A New Method for Field Calculation Using the Equivalent Electric Circuit”, in 13^rd COMPUMAG, 2001, pp. 232-233.